Answer:
[tex]y = -3x+11[/tex]
Step-by-step explanation:
I accept your challenge!
First we know that a equation of the line is a linear equation, and its equation is:
[tex]y = mx+b[/tex]
[tex]m: \text{slope}\\b: \text{y-intercept}[/tex]
In this context, the slope, defined as the steepness of a line is characterized as the ratio of RISE (the difference in the y-coordinates, the vertical change) over the RUN (the difference in x-coordinates, the horizontal change).
[tex]$m=\frac{\text{change in y}}{\text{change in x}}=\frac{\Delta y}{\Delta x}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} $[/tex]
Once we know two points where the line goes through, we can get the slope, once we know the change in y and x.
I will take [tex](3,2)[/tex] as Point 1 and [tex](4,-1)[/tex] as Point 2.
So, [tex]x_{1}=3 \text{ and } y_{1}=2\\x_{2}=4 \text{ and } y_{2}=-1[/tex]
[tex]$m=\frac{\text{change in y}}{\text{change in x}}=\frac{\Delta y}{\Delta x}=\frac{-1-2}{4-3} $[/tex]
[tex]$m=\frac{-3}{1}=-3 $[/tex]
Now we have to find the y-intercept:
To do so, think about the the points given and the nearly finished equation, we can find b with those two informations.
Our currently equation of the line is:
[tex]y = -3x+b[/tex]
Using the points, take Point 1 as an example, it says that when [tex]x = 3, y = 2[/tex], so plugging it in the equation:
[tex]2 = -3(3)+b\\2 = -9+b\\11 = b[/tex]
Taking the Point 2
[tex]-1 = -3(4)+b\\-1 = -12+b\\11 = b[/tex]
Now we found [tex]b[/tex]! The equation is complete!
[tex]y = -3x+11[/tex]
PLEASE HURRY IM IN A RUSH!!!!!!! 100 POINTS!
Which equation represents the function graphed on the coordinate plane? g(x) = |x + 1| + 3 g(x) = |x + 3| – 1 g(x) = |x – 1| + 3 g(x) = |x + 3| + 1
Answer:
x + 1| + 3 g(x) = |x + 3| – 1 g(x) = |x – 1| + 3 g(x) = |x + 3| + 1
Step-by-step explanation:
Answer:
g(x) = |x – 1| + 3
Step-by-step explanation:
Definitely right!
The functions f(x) and g(x) are described using the following equation and table:
f(x) = 3(1.02)x
_______
x g(x)
−1 −4
0 6
1 8
2 10
_______
Which statement best compares the y-intercepts of f(x) and g(x)?
A: The y-intercept of f(x) is equal to the y-intercept of g(x).
B: The y-intercept of f(x) is equal to 2 times the y-intercept of g(x).
C: The y-intercept of g(x) is equal to 2 times the y-intercept of f(x).
D: The y-intercept of g(x) is equal to 2 plus y-intercept of f(x).
Answer: D) The y-intercept of g(x) is equal to 2 times the y-intercept of f(x)
Answer:
D
Step-by-step explanation:
Have a good day! :D
Which of these chess pieces starts on squares a1 and h1, and a8 and h8?
Answer: Each player has two rooks (formerly also known as castles), which begin the game on the corner squares a1 and h1 for White, a8 and h8 for Black.
Step-by-step explanation: Mark me as brainliest
When Joe’s loses a golf ball he takes another from the box which graph models this relationship
what is the value of x?
Answer:7
Step-by-step explanation:
1. A filing cabinet measures 5
feet high by 18 inches wide by
2 feet deep. What is the
volume of the filing cabinet?
Answer:
180 in^3
Step-by-step explanation:
5•18=90in^2
90•2=180in^3
The formula for volume of a rectangular prism is V =
lwh.
The length of the prism is
_in.
The width of the prism is
_in.
The height of the prism is
_in.
The volume of the prism is
_in. 3
[tex]volume = lwh \\ = 15 \times 4 \times 5 \\ = 300 {in}^{3} [/tex]
hope this helps
brainliest appreciated
Good luck! have a nice day!
Answer:
The length of the prism is
✔ 15
in.
The width of the prism is
✔ 4
in.
The height of the prism is
✔ 5
in.
The volume of the prism is
✔ 300
in.3.
Step-by-step explanation:
On EDG assignment
When you play with dice in a board game, they are in the shape of what?
Faces/ Sides Shape
6 Cube
8 Octahedron
10 Pentagonal trapezohedron
12 Dodecahedron
Answer:
They are in the shape of a cube
Step-by-step explanation:
A pizza store charges $5 for delivery and $12 for p pizzas. How much does it cost to have 3 pizzas delivered?
Answer:
$41
Step-by-step explanation:
If we multiply 3 times 12 equals 36 plus $5 for delivery which equals $41.
Hope this helps!!! PLZ MARK BRAINLIEST!!
Answer:
41$
Step-by-step explanation:
12$ * 3 + 5$ = 41$
(would really appreciate the brainliest)
How do I find the surface area?
Answer:
Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.
Step-by-step explanation:
What is the vertex of the function?
Consider the quadratic function
f(x) = x2 - 8x -9
Vertex (
Answer:
(4,-25)
Step-by-step explanation:
I graphed this on the desmos graphing calculator.
A train is traveling at 30 miles per hour. The train is supposed to stop at 1:35 WHY is the train?
Answer:
i don't under stand this question but i think its because its supposed to stop at a certain time
Step-by-step explanation:
Answer:
The train is used to transfer people and instead of roads it uses railroad tracks. The train knows the way.
Step-by-step explanation:
what is 2 times 8/10???
So the right answer is 8/5
Look at the attached picture
Hope it will help you
Good luck on your assignment
Think of the 2 in this problem as 2/1.
So we have 2/1 × 8/10.
Now we can cross-cancel the 2 and 10 to 1 and 5.
So we have 1/1 × 8/5 which is 8/5.
is this relation a function?
Answer:no
Step-by-step explanation:
A function must have each x value map onto 1 y value. The x value 11 maps to two y values (1,3)
The following graph represents the hourly commission of a home appliance salesperson, y, based on the number of salespeople that are
working the showroom floor, x. The graph of the hourly commission of the salesperson is a quadratic function. What is the equation for
the function in standard form if the vertex is 6.5,42.25 and the origin is the only other known point?
We have been given graph of a downward opening parabola with vertex at point [tex](6.5,42.25)[/tex]. We are asked to write equation of the parabola in standard form.
We know that equation of parabola in standard form is [tex]f(x)=ax^2+bx+c[/tex].
We will write our equation in vertex form and then convert it into standard form.
Vertex for of parabola is [tex]y=a(x-h)^2+k[/tex], where point (h,k) represents vertex of parabola and a represents leading coefficient.
Since our parabola is downward opening so leading coefficient will be negative.
Upon substituting coordinates of vertex and point (0,0) in vertex form, we will get:
[tex]0=-a(0-6.5)^2+42.25[/tex]
[tex]0=-a(42.25)+42.25[/tex]
[tex]-42.25=-a(42.25)+42.25-42.25[/tex]
[tex]-42.25=-42.25a[/tex]
[tex]a=1[/tex] Divide both sides by [tex]-42.25[/tex]
So our equation in vertex form would be [tex]f(x)=-(x-6.5)^2+42.25[/tex].
Let us convert it in standard from.
[tex]f(x)=-(x^2-13x+42.25)+42.25[/tex]
[tex]f(x)=-x^2+13x-42.25+42.25[/tex]
[tex]f(x)=-x^2+13x[/tex]
Therefore, the equation of function is standard form would be [tex]f(x)=-x^2+13x[/tex].
Which of the following is not a translation of the algebraic expression 12.4 - 36 into words?
12.4 minus 3 times a number
The product of 3 and a number subtracted from 12.4
The difference of 12.4 and a quotient of and a number
The difference of 12.4 and 3 times a number
Answer:
The difference of 12.4 and a quotient of and a number because when it says quotient it is talking about division and you are not dividing anything.
Step-by-step explanation:
"The difference of 12.4 and a quotient of and a number" is not a translation of the algebraic expression.
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.
Given:
An algebraic expression 12.4 - 36.
The equivalent expressions are:
1). 12.4 minus 3 times a number 6.
Let a = 6
That means, 12.4 - 3(6)
2). The product of 3 and a number subtracted from 12.4.
Let a = 6
That means, 12.4 - 3(6)
3). The difference of 12.4 and a quotient of and a number.
That means,
12.4 - 3/6
4). The difference of 12.4 and 3 times a number.
Let a = 6
That means, 12.4 - 3(6)
Therefore, "The difference of 12.4 and a quotient of and a number" is a required expression.
To learn more about the expression;
brainly.com/question/24242989
#SPJ6
If in a crowd, each person takes about 2.5 ft2 to stand comfortably, estimate the size of a crowd that is 10 feet deep on both sides of a street for a mile and is filled with people.
Hi!
I'm Happy to help you today!
The answer would be B. or 42,240!
The reason is because if you do the math and all that it gives you the answer of 42,240 or B. !
-LimitedLegxnd
-If you like my answer make sure to hit that Heart! Also to show others how helpful my answer is click the stars!
-Question asker if you really liked my answer mark mine brainliest!
3/12 - 1/3 =
Please answer
Answer:
-0.0833
Step-by-step explanation:
Drag and drop an answer to each box to correctly explain the derivation of the formula for the volume of a pyramid.
Answer:
1 to 3 and V= 1/2 Bh
Step-by-step explanation:
the pyramid is like a triangle there is three sides. There is only one way of the whole pyramid you can cut.
Write the equation of the graph which is the reflection of y=−|x−1|−1 about the origin
Answer:
f(x) = |x + 1| + 1
Step-by-step explanation:
A reflection over the y-axis followed by a reflection over x-axis is equivalent to a reflection about origin.
f(x) = -|x-1| -1
reflection over the x-axis:
-f(x) = (-1)*(-|x-1| -1) = |x-1| +1
reflection over the y-axis of the previous function:
-f(-x) = |-x-1| +1 = |x + 1| + 1
which is the reflection of f(x) about the origin
help! will mark brainliest:)
Answer:
x<-1 and x>2
Step-by-step explanation:
The domain is the values that input can b, in this case x
X can be less than -1
x< -1
X can be greater than 2
x>2
x<-1 and x>2
how does 10 to the power of -3 compare to 2 to the power of -3
Answer:
10^-3 is 1/1000 and 2^-3 is 1/16
Step-by-step explanation
Answer:
I think the correct answer is 10^-3 1/1000 and 2^-3 is 1/16
Step-by-step explanation:
-edit: The other user copied my answer! ^_^
Two lines meet at a point. List the relevant angle relationship in the diagram. Set up and solve an equation to find the value of . Find the measurement of one of the vertical angles.
Answer:
Measure of one Vertical Angle; 96°
Step-by-step explanation:
Here the measure of one of these vertical angles ⇒ 96°, explained in the attachment below;
PLEASE ANSWER THIS QUESTION CORRECTLY AND ILL MARK YOU AS THE BRAINLIEST
Answer:
4. (x+3)^2 =16
Step-by-step explanation:
Rewrite x^2 +6x -7 = 0 in quadratic form by compliting the square
x^2 +6x = 7 divide 6 by 2 ans square so 6/2 = 3, [tex]3^{2} = 9[/tex] add 9 on each side
x^2 +6x +9 = 7+9 =16 remember that [tex](a + b)^{2} = a^{2} +2ab + b^{2}[/tex]
[tex](x +3)^{2} = 16[/tex]
use this site if it helps for your question desmos.com
50 points!! A scale drawing of a building needs to be made using the scale 1 in = 190 ft. How tall will the building in the scale be if the building 2090 ft tall?
Answer:
11 inches tall
2090/190ft =11 inches
1inch=190ft
11x190
2090ft
Step-by-step explanation:
Answer:
11 inches
Step-by-step explanation:
We can use ratios to solve
1 inch x inches
------------ = --------------
190 ft 2090 ft
Using cross products
1 * 2090 = 190 * x
Divide each side by 90
2090/190 = 190x/190
11 =x
11 inches
A sphere has a diameter of 12 ft. What is the volume of the sphere? Give the exact value in terms of .
aft
Answer:
288π
That is exact value in terms of pi.
Step-by-step explanation:
So if the diameter is 12, the radius is 6.
The volume of a sphere is [tex]\frac{4}{3} \pi r^3[/tex]
Since r = 6, the volume is [tex]\frac{4}{3} * 216\pi[/tex]
Which is 288π
Answer:
904.78 is the answer
volume = 4/3 π r cubed
In a class of 150 students, 95 are taking math (M), 77 are taking science (S), and 53 are taking both math and science. One student is picked at random. Find the probability.
P(taking math or science or both)=????????????
(Round to three decimal places as needed.)
All my points ;c
31%is the answer i think
please help me with steps
Answer:
x = (3 − √5) / 2, (3 + √5) / 2, and 1
Step-by-step explanation:
Using rational root theorem, ±1 are possible roots. By trial and error, we find that +1 is a root. Therefore, x − 1 is a factor. Knowing this, we can use grouping or long division. Using grouping:
x⁴ − 5x³ + 8x² − 5x + 1 = 0
x⁴ − 5x³ + 4x² + 4x² − 5x + 1 = 0
x² (x² − 5x + 4) + 4x² − 5x + 1 = 0
x² (x − 4) (x − 1) + (4x − 1) (x − 1) = 0
(x² (x − 4) + 4x − 1) (x − 1) = 0
(x³ − 4x² + 4x − 1) (x − 1) = 0
Repeating the process, possible rational roots of x³ − 4x² + 4x − 1 are ±1. We already know -1 isn't a root. By trial and error, we find that +1 is again a root. Using grouping to factor:
(x³ − 4x² + 3x + x − 1) (x − 1) = 0
(x (x² − 4x + 3) + x − 1) (x − 1) = 0
(x (x − 3) (x − 1) + x − 1) (x − 1) = 0
(x (x − 3) + 1) (x − 1) (x − 1) = 0
(x² − 3x + 1) (x − 1)² = 0
To find the roots of x² − 3x + 1, we use the quadratic formula.
x = [ -(-3) ± √((-3)² − 4(1)(1)) ] / 2(1)
x = [ 3 ± √(9 − 4) ] / 2
x = (3 ± √5) / 2
So the roots are x = (3 − √5) / 2, (3 + √5) / 2, and 1.
To rationalize the denominator of StartFraction 2 StartRoot 10 EndRoot Over 3 StartRoot 11 EndRoot EndFraction, you should multiply the expression by which fraction? StartFraction StartRoot 10 EndRoot Over StartRoot 10 EndRoot EndFraction StartFraction StartRoot 11 EndRoot Over StartRoot 11 EndRoot EndFraction StartFraction 2 minus StartRoot 10 EndRoot Over 2 minus StartRoot 10 EndRoot EndFraction StartFraction 3 minus StartRoot 11 EndRoot Over 3 minus StartRoot 11 EndRoot EndFraction
Step-by-step explanation:
bbbbbbbbbbbbbbb,bbbbbb
To rationalize the denominator of [tex]\frac{2\sqrt{10} }{3\sqrt{11} }[/tex] you should multiply the expression by [tex]\frac{\sqrt{11} }{\sqrt{11} }[/tex]
Given the surd function:
[tex]\frac{2\sqrt{10} }{3\sqrt{11} }[/tex]Rationalizing surd functions means multiplying the numerator and denominator of such function by the conjugate of the denominator.For the surd function given, to rationalize it, we only need to multiply the numerator and denominator by √11 as shown:
[tex]=\frac{2\sqrt{10} }{3\sqrt{11} }\times \frac{\sqrt{11} }{\sqrt{11} } \\=\frac{2\sqrt{110}}{3(11)}\\= \frac{2\sqrt{110}}{33}\\[/tex]
Hence we can conclude that to rationalize the denominator of [tex]\frac{2\sqrt{10} }{3\sqrt{11} }[/tex] you should multiply the expression by [tex]\frac{\sqrt{11} }{\sqrt{11} }[/tex]
Learn more about surd functions here: https://brainly.com/question/24380382
Could I please have some help? Thanks
Answer:
D
Step-by-step explanation:
There is a common difference d between consecutive terms, that is
d = - 1 [tex]\frac{1}{2}[/tex] -(- [tex]\frac{1}{2}[/tex] ) = - 1
d = - 2 [tex]\frac{1}{2}[/tex] - (- 1 [tex]\frac{1}{2}[/tex] ) = - 1
d = - 3 [tex]\frac{1}{2}[/tex] - (- 2 [tex]\frac{1}{2}[/tex] ) = - 1
This indicates the sequence is arithmetic with explicit formula
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - [tex]\frac{1}{2}[/tex] and d = - 1 , thus
[tex]a_{n}[/tex] = - [tex]\frac{1}{2}[/tex] - 1 (n - 1) = - [tex]\frac{1}{2}[/tex] - n + 1 = [tex]\frac{1}{2}[/tex] - n , where n = 1, 2, 3, 4, ......